Invertibility of Sobolev mappings under minimal hypotheses

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8 Scopus citations


We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W1, n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

Original languageEnglish (US)
Pages (from-to)517-528
Number of pages12
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number2
StatePublished - 2010


  • Differential inclusion
  • Finite distortion
  • Local homeomorphism

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics


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